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Determine o valor de x na figura a seguir

To determine the value of \( x \) in the given figure, we need to use the geometric properties of parallel lines and transversals.

From the figure:
- There are three parallel lines labeled \( a \), \( b \), and \( c \).
- A transversal intersects the parallel lines at various points, forming the following angles:
  - \( x \) (the unknown angle),
  - 3,
  - 5,
  - \( x + 4 \).

### Step-by-step solution:

1. **Using the properties of parallel lines**:
   - The angles \( x \) and \( 5 \) are **corresponding angles**, meaning they are equal:
   \[
   x = 5
   \]

   - The angles \( 3 \) and \( x + 4 \) are also **corresponding angles**, so:
   \[
   3 = x + 4
   \]

2. **Solving for \( x \)**:
   From the equation \( 3 = x + 4 \), solve for \( x \):
   \[
   3 - 4 = x
   \]
   \[
   x = -1
   \]

Thus, the value of \( x \) is \( -1 \).

If you have any questions or need further clarification, feel free to ask! Here are some related questions:

1. What are the properties of corresponding angles?
2. How do we identify alternate interior angles?
3. Can you explain the concept of parallel lines and transversals?
4. How do you solve systems of equations involving geometric relationships?
5. What are the steps to verify angle relationships in a complex figure?

**Tip:** In problems involving parallel lines and transversals, always look for corresponding and alternate interior angles, as they often provide a direct path to solving for unknowns.

Determine o valor de x na figura a seguir.

Learn how to determine the value of x using the properties of parallel lines and corresponding angles. This problem involves solving equations and understanding theorems related to geometry. Suitable for students in Grades 7-9.

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